In the ultrahigh-speed communication at 40 Gbps and 100 Gbps, there is the problems of an insufficient optical signal-to-noise ratio (OSNR) and a linearity distortion of wavelength dispersion etc. The digital coherent reception system using an analog-to-digital converter has attracted considerable attention as a solution for the problems.
Used in the transmission at 100 Gbps or higher is polarization orthogonal modulation for modulating data independent of the polarization having vertical polarization orthogonal to horizontal polarization. Since the polarization state in optical fiber may cause a high-speed polarization fluctuation at 10 KHz or higher, it is necessary for a reception unit to perform high-speed polarization control for separating a vertical polarization signal and a horizontal polarization signal while following the high-speed polarization fluctuation. The adaptive equalizer is used for high-speed polarization control.
FIG. 1 illustrates an example of an adaptive equalizer 11. The adaptive equalizer 11 has four FIR (finite impulse response) filters 12-1 through 12-4 and a filter coefficient application control circuit 13.
In FIG. 1, a horizontal signal component Eh=(Ih, Qh) and a vertical signal component Ev=(Iv, Qv) on the input side of the adaptive equalizer 11 are signals including polarization fluctuation components. A horizontal signal component Eh′=(Ih′, Qh′) and a vertical signal component Ev′=(Iv′, Qv′) on the output side are polarization-separated signals.
Each of the FIR filters 12-1 and 12-2 receives the horizontal signal component Eh=(Ih, Qh) and the vertical signal component Ev=(Iv, Qv), and a signal obtained by combining the components is output as a vertical signal component E′v=(I′v, Q′v).
The filter coefficient application control circuit 13 controls the tap coefficient and the combination ratio of the four FIR filters 12-1 through 12-4.
The above-mentioned adaptive equalizer 11 can adaptively update the tap coefficient and the combination ratio of the FIR filters in real time in an update time sufficiently higher than the polarization fluctuation of optical fiber, thereby realizing a stable reception state against the fluctuation of the polarization state and the PMD. The PMD refers to polarization mode dispersion.
Proposed as adaptive equalization methods for the adaptive equalizer are a method using a training symbol, decision directed-least mean squares (DD-LMS), a constant modulus algorithm (CMA method) method, etc. The CMA method is a type of blind equalization not requiring a training symbol, and a method of controlling the tap coefficient of a filter so that the peak power of a signal after the adaptive equalization can be constant. The CMA method has a merit of having a simpler circuit than the method of using a training symbol and the DD-LMS, and being capable of converging independent of a tap coefficient initial value.
FIG. 2 is a configuration of an adaptive equalizer using the CMA method. An adaptive equalizer 21 has four FIR filters 22-1 through 22-4 and a filter coefficient application control circuit 23. The tap coefficient of the FIR filter 22-1 is expressed as hhh, the tap coefficient of the FIR filter 22-2 is expressed as hvh, the tap coefficient of the FIR filter 22-3 is expressed as hhv, and the tap coefficient of the FIR filter 22-4 is expressed as hvv.
The update equation of the tap coefficient of the filter in the CMA method is expressed as follows.H(n+1)=H(n)−μ·rn*(|yn|2−γ)yn rn*=(Eh*,Ev*)=((Ih,−Qh),(Iv,−Qv)): FIR input signal yn=(Eh′,Ev′): FIR output signalH (n): tap coefficient, γ: target amplitude constant
The filter coefficient application control circuit 23 controls the tap coefficient of the filter so that the peak power of the signal can be constant by the equation above.
When the digital signal processing exceeding 100 Gbps is realized using the CMOS circuit, a number (for example, more than 500 lanes) of circuits are provided in parallel, some of which are selected and fed back. In this case, depending on the initial value of the tap coefficient of a FIR filter, the FIR filter may converge to a local minimum solution, and a waveform may not be correctly formed.
FIG. 3 illustrates the constellations on the horizontal polarization side and the vertical polarization side. As illustrated in FIG. 3, the constellation on the horizontal (H) polarization side converges around the center, and the horizontally polarization side converges to a local minimum solution.
To detect the convergence to a local minimum solution using a forward error correction (FEC) counter etc., it is necessary to complete the extraction of a frame by terminating the processes of a local emission frequency offset estimation unit, a carrier wave phase estimation unit, a determination unit, a frame synchronization unit, etc. Therefore, there has been the problem that it takes a long time to detect the convergence to a local minimum solution (hereafter referred to as a local convergence).
In addition, there has been the problem with the CMA method that the uniquness of a convergent solution is not guaranteed. That is, with the adaptive equalizer using the CMA method, there are cases in which a horizontal polarization signal and a vertical polarization signal can be separated into two different signals, and in which the same polarization signal is output separated into a horizontal polarization signal and a vertical polarization signal.
To solve the above-mentioned problem in the CMA method, the logarithm partial differentiation value of the target probability density function of a separation output signal of a polarization separator for polarization-separating an input signal is calculated, and based on the logarithm polarization differentiation value, the inclination of the target optimum function for optimizing the distribution of a multiple output signal is calculated. Furthermore, the technology of avoiding the equivalence convergence by updating the coefficient of a filter based on the inclination obtained by the calculation is known (for example, patent document 1).
In addition, a technology of calculating one tap coefficient of a FIR filter, which outputs a horizontal polarization signal or a vertical polarization signal, from another tap coefficient is known. Even when equivalence convergence occurs, the equivalence convergence can be avoided by regenerating a tap coefficient (for example, non-patent document 1).